First and for all, make sure your website is ready and optimized before you start getting the attention.
Associate the website with the owner or key figures of the company
Search for mentions of competitors whether lists, directories and comparison and get your name there
Search for list or directories of local organisations in your area of operation or with the same attributes. Also local chamber of commerce, newspaper, sport club offering a discount...)
Guest post on popular and relevant blogs, build relationships with influencers. Check for dead links
Get reviews from online influencers, or independent review sites such as G2Crowd
Monitor non linked mentions of the website and get them made as links. This however should not be too much of a priority as there are more signals which are pointing to the fact these mentions are already considered b Google as trust ones
Useful tools for this research: Majestic SEO and Open Site Explorer (Moz). SEMRush to identify the top ranking pages on a site
It should be partially used to figure out a few choice bits to add to your own strategy, not a massive pattern to copy. For instance:
Mostly to drive traffic and for brand awareness as links are normally nofollow. Do create content for forum and point it, participating in relevant other conversations to avoid focusing only self-promotion.
Track visitors, conversions and traffic. Compare Keywords rankings
Evaluate how any improvements in ranking improves or not your goals for conversion, maybe the ones you are targeting are not the best ones.